GATE 2023 MT – Question 5
A line of symmetry divides a figure into two parts that are mirror images about that line. The figure consists of 16 unit squares, three already black. What minimum number of additional squares must be coloured black so that both PQ and MN are lines of symmetry? The figure is representative.
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Correct answer: (C) 5
Explanation
Number the rows from top to bottom and columns from left to right. The initial black squares are $(1,3),(2,1),(4,3)$. Closure under the vertical reflection and the diagonal reflection gives $(1,2),(1,3),(2,1),(2,4),(3,1),(3,4),(4,2),(4,3)$. All eight must be black. Three are already black, so add **5, C**.